Chris@16: // Copyright 2004 The Trustees of Indiana University.
Chris@16: 
Chris@16: // Distributed under the Boost Software License, Version 1.0.
Chris@16: // (See accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: //  Authors: Douglas Gregor
Chris@16: //           Andrew Lumsdaine
Chris@16: #ifndef BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP
Chris@16: #define BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP
Chris@16: 
Chris@16: #include <boost/graph/betweenness_centrality.hpp>
Chris@16: #include <boost/graph/graph_traits.hpp>
Chris@16: #include <boost/graph/graph_utility.hpp>
Chris@16: #include <boost/pending/indirect_cmp.hpp>
Chris@16: #include <algorithm>
Chris@16: #include <vector>
Chris@16: #include <boost/property_map/property_map.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16: /** Threshold termination function for the betweenness centrality
Chris@16:  * clustering algorithm.
Chris@16:  */
Chris@16: template<typename T>
Chris@16: struct bc_clustering_threshold
Chris@16: {
Chris@16:   typedef T centrality_type;
Chris@16: 
Chris@16:   /// Terminate clustering when maximum absolute edge centrality is
Chris@16:   /// below the given threshold.
Chris@16:   explicit bc_clustering_threshold(T threshold) 
Chris@16:     : threshold(threshold), dividend(1.0) {}
Chris@16:   
Chris@16:   /**
Chris@16:    * Terminate clustering when the maximum edge centrality is below
Chris@16:    * the given threshold.
Chris@16:    *
Chris@16:    * @param threshold the threshold value
Chris@16:    *
Chris@16:    * @param g the graph on which the threshold will be calculated
Chris@16:    *
Chris@16:    * @param normalize when true, the threshold is compared against the
Chris@16:    * normalized edge centrality based on the input graph; otherwise,
Chris@16:    * the threshold is compared against the absolute edge centrality.
Chris@16:    */
Chris@16:   template<typename Graph>
Chris@16:   bc_clustering_threshold(T threshold, const Graph& g, bool normalize = true)
Chris@16:     : threshold(threshold), dividend(1.0)
Chris@16:   {
Chris@16:     if (normalize) {
Chris@16:       typename graph_traits<Graph>::vertices_size_type n = num_vertices(g);
Chris@16:       dividend = T((n - 1) * (n - 2)) / T(2);
Chris@16:     }
Chris@16:   }
Chris@16: 
Chris@16:   /** Returns true when the given maximum edge centrality (potentially
Chris@16:    * normalized) falls below the threshold.
Chris@16:    */
Chris@16:   template<typename Graph, typename Edge>
Chris@16:   bool operator()(T max_centrality, Edge, const Graph&)
Chris@16:   {
Chris@16:     return (max_centrality / dividend) < threshold;
Chris@16:   }
Chris@16: 
Chris@16:  protected:
Chris@16:   T threshold;
Chris@16:   T dividend;
Chris@16: };
Chris@16: 
Chris@16: /** Graph clustering based on edge betweenness centrality.
Chris@16:  * 
Chris@16:  * This algorithm implements graph clustering based on edge
Chris@16:  * betweenness centrality. It is an iterative algorithm, where in each
Chris@16:  * step it compute the edge betweenness centrality (via @ref
Chris@16:  * brandes_betweenness_centrality) and removes the edge with the
Chris@16:  * maximum betweenness centrality. The @p done function object
Chris@16:  * determines when the algorithm terminates (the edge found when the
Chris@16:  * algorithm terminates will not be removed).
Chris@16:  *
Chris@16:  * @param g The graph on which clustering will be performed. The type
Chris@16:  * of this parameter (@c MutableGraph) must be a model of the
Chris@16:  * VertexListGraph, IncidenceGraph, EdgeListGraph, and Mutable Graph
Chris@16:  * concepts.
Chris@16:  *
Chris@16:  * @param done The function object that indicates termination of the
Chris@16:  * algorithm. It must be a ternary function object thats accepts the
Chris@16:  * maximum centrality, the descriptor of the edge that will be
Chris@16:  * removed, and the graph @p g.
Chris@16:  *
Chris@16:  * @param edge_centrality (UTIL/OUT) The property map that will store
Chris@16:  * the betweenness centrality for each edge. When the algorithm
Chris@16:  * terminates, it will contain the edge centralities for the
Chris@16:  * graph. The type of this property map must model the
Chris@16:  * ReadWritePropertyMap concept. Defaults to an @c
Chris@16:  * iterator_property_map whose value type is 
Chris@16:  * @c Done::centrality_type and using @c get(edge_index, g) for the 
Chris@16:  * index map.
Chris@16:  *
Chris@16:  * @param vertex_index (IN) The property map that maps vertices to
Chris@16:  * indices in the range @c [0, num_vertices(g)). This type of this
Chris@16:  * property map must model the ReadablePropertyMap concept and its
Chris@16:  * value type must be an integral type. Defaults to 
Chris@16:  * @c get(vertex_index, g).
Chris@16:  */
Chris@16: template<typename MutableGraph, typename Done, typename EdgeCentralityMap,
Chris@16:          typename VertexIndexMap>
Chris@16: void 
Chris@16: betweenness_centrality_clustering(MutableGraph& g, Done done,
Chris@16:                                   EdgeCentralityMap edge_centrality,
Chris@16:                                   VertexIndexMap vertex_index)
Chris@16: {
Chris@16:   typedef typename property_traits<EdgeCentralityMap>::value_type
Chris@16:     centrality_type;
Chris@16:   typedef typename graph_traits<MutableGraph>::edge_iterator edge_iterator;
Chris@16:   typedef typename graph_traits<MutableGraph>::edge_descriptor edge_descriptor;
Chris@16:   typedef typename graph_traits<MutableGraph>::vertices_size_type
Chris@16:     vertices_size_type;
Chris@16: 
Chris@16:   if (has_no_edges(g)) return;
Chris@16: 
Chris@16:   // Function object that compares the centrality of edges
Chris@16:   indirect_cmp<EdgeCentralityMap, std::less<centrality_type> > 
Chris@16:     cmp(edge_centrality);
Chris@16: 
Chris@16:   bool is_done;
Chris@16:   do {
Chris@16:     brandes_betweenness_centrality(g, 
Chris@16:                                    edge_centrality_map(edge_centrality)
Chris@16:                                    .vertex_index_map(vertex_index));
Chris@16:     std::pair<edge_iterator, edge_iterator> edges_iters = edges(g);
Chris@16:     edge_descriptor e = *max_element(edges_iters.first, edges_iters.second, cmp);
Chris@16:     is_done = done(get(edge_centrality, e), e, g);
Chris@16:     if (!is_done) remove_edge(e, g);
Chris@16:   } while (!is_done && !has_no_edges(g));
Chris@16: }
Chris@16: 
Chris@16: /**
Chris@16:  * \overload
Chris@16:  */ 
Chris@16: template<typename MutableGraph, typename Done, typename EdgeCentralityMap>
Chris@16: void 
Chris@16: betweenness_centrality_clustering(MutableGraph& g, Done done,
Chris@16:                                   EdgeCentralityMap edge_centrality)
Chris@16: {
Chris@16:   betweenness_centrality_clustering(g, done, edge_centrality,
Chris@16:                                     get(vertex_index, g));
Chris@16: }
Chris@16: 
Chris@16: /**
Chris@16:  * \overload
Chris@16:  */ 
Chris@16: template<typename MutableGraph, typename Done>
Chris@16: void
Chris@16: betweenness_centrality_clustering(MutableGraph& g, Done done)
Chris@16: {
Chris@16:   typedef typename Done::centrality_type centrality_type;
Chris@16:   std::vector<centrality_type> edge_centrality(num_edges(g));
Chris@16:   betweenness_centrality_clustering(g, done, 
Chris@16:     make_iterator_property_map(edge_centrality.begin(), get(edge_index, g)),
Chris@16:     get(vertex_index, g));
Chris@16: }
Chris@16: 
Chris@16: } // end namespace boost
Chris@16: 
Chris@16: #endif // BOOST_GRAPH_BETWEENNESS_CENTRALITY_CLUSTERING_HPP